Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm

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Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm

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Preeti Ranjan Sahu ∗ , Prakash Kumar Hota, Sidhartha Panda

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Dept. of Electrical Engg., Veer Surendra Sai University of Technology (VSSUT), Burla, Odisha, India Received 1 April 2017; received in revised form 13 February 2018; accepted 21 February 2018

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Abstract In this paper, a designing process of fractional order multi input single output (MISO) type static synchronous series compensator (SSSC) using whale optimization algorithm (WOA) is detailed. The controller design task is taken as an optimization task and WOA is utilized to tune the controller parameters. The effectiveness of the proposed controllers is assessed under various disturbances for both single-machine infinite-bus and multi-machine power systems. To demonstrate the superiority of MISO controller for SSSC, results are compared with differential evolution and particle swarm optimization based conventional single input single output (SISO) structured SSSC controllers. It is observed that the MISO control approach yield better damping characteristic than SISO methodologies. © 2018 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Fractional order (FO) controller; Power system stability; Static synchronous series compensator (SSSC); Whale optimization algorithm (WOA)

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1. Introduction In recent days, the significance of dynamic and transient stability worth utmost importance in order to achieve increased power transfer. The flexible AC transmission system (FACTS) controllers can possibly improve the transient and dynamic stability margin (Hingorani and Gyugyi, 2000). Static synchronous series compensator (SSSC) is one of the primary individuals from arrangement FACTS controller. SSSC has the ability to change its reactance characteristics from capacitive to inductive without changing the amount of line current that’s why it is very efficient in controlling power flow in a transmission line (Gyugyi et al., 1997). SSSC is additionally invulnerable to established system ∗

Corresponding author. E-mail addresses: [email protected] (P.R. Sahu), p [email protected] (P.K. Hota), panda [email protected] (S. Panda). Peer review under the responsibility of Electronics Research Institute (ERI).

https://doi.org/10.1016/j.jesit.2018.02.008 2314-7172/© 2018 Production and hosting by Elsevier B.V. on behalf of Electronics Research Institute (ERI). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Nomenclature VS Sending end voltage of generator (p.u.) Receiving end voltage of infinite-bus (p.u.) VR V1 and V2 Bus voltages (p.u.) VDC DC voltage source of the SSSC converter (p.u.) VCNV Output voltage of the SSSC converter (p.u.) PL Real power flow (MW) PL Change in real power flow (p.u.) Speed deviation (p.u.) ω TSN Sensor time constant (s) TTD Delay time constant (s) KPL and KPR Proportional gain KDL and KDR Derivative gain K Fractional order gain TWL and TWR Washout time constants (s) T1L , T2L , T3L , T4L , T1R , T2R , T3R , T4R Phase compensation time constants (s) Reference injected voltage (p.u.) Vqref Vq1 , Vq2 Change in the injected voltage of SSSC (p.u.)

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resonances. To enhance the power transfer controllability, a SSSC controller is inserted in transmission line of power system which can be used to create an additional damping controller for the SSSC to damp the power system oscillation (Wang, 2000). A conventional lead-lag controller structure is favoured by the utilities of power system due to the simplicity of on-line tuning and absence of confirmation of the stability by some versatile or variable structure methods (Panda et al., 2010, 2008; Panda, 2009). The issue of controller parameter tuning is a troublesome assignment. Several methodologies have been proposed to design FACTS-based auxiliary damping controller. Some of these methodologies are genetic algorithm (GA) (Panda et al., 2010), particle swarm optimization (PSO) (Panda et al., 2008), multi-objective optimization algorithm (Panda, 2009), differential evolution (DE) (Panda, 2011) and so forth. Whale optimization algorithm (WOA) is a recently proposed population based meta-heuristic technique inspired by hunting behaviour of whales (Mirjalili and Lewis, 2016). The algorithm uses three operators the search for prey, encircling prey, and bubblenet foraging behaviour of whales for optimization. The superiority of WOA over PSO, gravitational search algorithm (GSA), DE, Fast Evolutionary Programming (FEP), and Evolution Strategy with Covariance Matrix Adaptation (CMAES) has been demonstrated (Mirjalili and Lewis, 2016). In view of the above, an attempt has been made in this paper for the use of a WOA optimized FO MISO of a SSSC controller. Most of the works on damping controller reported in literature employ single input single output (SISO) controllers utilizing either input signal or remote signal (Wang, 2000; Panda et al., 2010, 2008; Panda, 2009; Panda, 2011; Mirjalili and Lewis, 2016). To minimize cost and improve reliability, input signal should ideally be locally assessable. But, local control signals may not contain the desired oscillation modes and hence compared to remote signals, they are not controllable and observable. In Panda and Yegireddy (2015), a multi input single output (MISO) SSSC based damping controller has been proposed using both local and remote signals. In this paper, a fractional order (FO) MISO controller using both local signal (tie-line power deviation signal) and remote signal (speed deviation signal) is proposed for SSSC based damping controller. The proposed controller parameters are optimized using WOA technique. The main contributions of the paper are: 1. A novel fractional order MISO controller is proposed for SSSC-based damping controller as an alternative to conventional SISO controllers proposed in the literature. 2. An innovative optimization technique based on WOA is employed to optimize the parameters of controller. Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 1. Single machine infinite bus power system with SSSC.

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In order to evaluate the performance of the proposed approach, two test systems are taken into consideration. The simulation results are compared with that of the results of published DE and PSO based SISO controllers for identical test systems.

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2. System under study

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2.1. Single-machine infinite bus power system with SSSC

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A single machine infinite bus (SMIB) control system shown in Fig. 1 is considered at first to design proposed FO MISO controller. In the studied power system, the generator is connected to the infinite bus by a double circuit transmission line. The generating system constitutes (i) hydraulic turbine and governor (HTG) and (ii) excitation system. The excitation system contains a DC exciter and voltage regulator, as per IEEE recommendation practice for Anon (2010). Also, a SSSC is assumed in the system to improve the stability.

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3. The proposed approach

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3.1. Fractional order controllers

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In recent times, there are expanding interests to upgrade the execution of conventional PID controllers by utilizing the idea of fractional analytics, where the requests of derivatives and integrals are non-integer type. The most basic type of FO PID controller is the PI␭ D␮ controller (Hamamci, 2007). It is seen from literature that FO PID controller gives additional freedom to tune the integral and derivatives and gives considerably more adaptability in PID control design. A number of methods have been utilized to tune the parameters of fractional controllers. In Biswas et al. (2009), enhanced DE procedure has been employed to optimize PI␭ D␮ controller based on dominant pole placement approach. Other tuning methods proposed in fundamental criteria based FOPID controller (Taher et al., 2016). Though, the stability and speed of response of the system is improved by the derivative mode yet it may deliver large size control output particularly when the input signal has sharp corners and contains noise. To overcome above issues, a filter is put on the derivative term and tunes its pole so that the chattering since of the noise does not happen as frequency noise is attenuated. In perspective of the over a filter is utilized for the derivative term in the current paper.

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3.2. Fractional order SSSC-based damping controller

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The proposed controller as shown in Fig. 2 comprises of two lead-lag components. Each lead-lag structure comprises of (i) gain blocks, (ii) washout block and (iii) phase compensation block. The phase lag between input and output is compensated with help of phase compensation block. The signal washout block with time constants work as high-pass filters to permit signals connected with oscillations in input signal as unaltered signals. Without the high-pass filters, consistent changes in input would modify the output. The phase compensation obstructs with time constants give the correct phase lead attributes to beat the phase lag amongst input and the output signals. Vqref represents the reference injected voltage as preferred by the steady state power flow control loop. In the present review Vqref is accepted steady during large disturbance transient period as it acts gradually. The key estimation Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 2. Configuration of proposed fractional order MISO SSSC-based damping controller.

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of compensation is obtained by the change in the injected voltage of SSSC Vq1 and Vq2 which is added to Vqref .

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3.3. Problem formulation

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The controllers organized for lead-lag, the time constants for washout TWL & TWR are generally pre-indicated (Panda et al., 2008). In the present review TWR = TWL = 10 s is used. Vq1 , Vq2 and Vref are constant during steady state conditions. The injected series voltage Vq is adjusted for power system oscillations damping and the effective Vq in the above condition during dynamic condition is given by: Vq = Vqref + Vq1 + V q2

(1)

The objective function as integral time absolute error of the speed deviations is given by Eq. (2). t

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J=

|ω| · t · dt

(2)

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where, ω is the deviation in speed; and t is the simulation time range. To ascertain the objective function, a fault is connected to the system under review and simulation for the time-domain model is performed. The plan issue is figured as the accompanying optimization issue: Minimize J

(3)

Subject to Ki min ≤ Ki ≤ Ki max T1i min ≤ T1i ≤ T1i max

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T2i min ≤ T2i ≤ T2i max

(4)

T3i min ≤ T3i ≤ T3i max T4i min ≤ T4i ≤ T4i max 103

where i = 1, 2 (i.e. L and R) for the two lead lag structured controllers. Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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4. Whale optimization algorithm (WOA) technique

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Whale optimization algorithm (WOA) is a recently proposed meta-heuristic algorithm based on social behaviour of whales (Mirjalili and Lewis, 2016). Humpback whales are among the biggest whales whose favourite prey are krill and small fish herds. The hunting process of humpback whales is based on bubble-net feeding approach method (Watkins and Schevill, 1979). The twisting bubble-net nourishing scheme is mathematically modelled in WOA.

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4.1. Optimization algorithm and mathematical model

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Here the scientific model of encircling prey, spiral bubble net encouraging move, and scan for prey is initially given, and then WOA technique is projected. 4.1.1. Encircling prey Humpback whale encircles the prey (small fishes) at that point overhauls its position towards the optimum solution over the course of increasing number of iteration from start to a maximum number of iteration.

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៝ X ៝ = |C. ៝ ∗ (t) − X(t)| ៝ D

(5)

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៝ D ៝ ∗ (t) − A. ៝ + 1) = X  X(t

(6)

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 and C  are coefficient vectors, X  is the position vector of the best arrangement where t shows the current iteration, A acquired in this way, X* is the position vector, · is element by element multiplication and | | is the absolute value. It  and C  are the vectors merits saying here that X∗ should be upgraded in every cycle if there is a superior solution. A considered as follows.

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 = 2a.r − a A

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(8)

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where a is linearly decreased from 2 to 0 over the course of iterations and r is a random vector in [0,1]. 4.1.2. Bubble-net attacking technique (exploitation stage) keeping in mind the end goal to scientifically display the bubble net behaviour of humpback whales, two methodologies are planned as takes after: 1. Shrinking encircling mechanism: This conduct is accomplished by diminishing the estimation of a in Eq. (7).  is likewise diminished bya. As such A  will be a random values in the Take note of that the fluctuation range of A  in range interim [−a, a] where a is diminished from 2 to 0 throughout cycles. Setting random values for a vector A between [−1, 1]. 2. Spiral updating arrangement: Scientific spiral condition for position update between humpback whale and prey that was helix-formed development given as takes after:  + 1) = D   .ebl . cos(2πl) + X  ∗ (t) X(t

(9)

  = |X  ∗ (t) − X(t)|  where D and shows the separation of the ith whale to the prey (best arrangement got as such), b is a steady to define the state of the logarithmic spiral; ‘.’ is a element to element multiplication and l is an arbitrary number in the range [−1, 1]. During optimization a certain probability is assumed in choosing between above two methods to update current position of humpback whale. Here it is assumed a probability of 50% in choosing either spiral model or the shrinking encircling mechanism. The mathematical model is given in Eq. (10)  ∗  D   (t) − A. if P < 0.5 X  + 1) = X(t (10)  ∗ (t) if P ≥ 0.5 D .ebl . cos(2␲l) + X where P is a arbitrary number in the range [0,1]. Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 3. Pseudo-code of the WOA technique. 142 143 144

4.1.3. Search for prey (Exploration phase)  vector can be utilized for exploration to search for prey; vector A  additionally takes the qualities more The A noteworthy than one or not as much as − 1. Exploration takes after two conditions: →

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 Xrand − X  = C.  D  + 1) = X(t

→ Xrand

 D  − A.

(11) (12)

→

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where Xrand is an arbitrary position vector (an irregular whale) looked over the present population. At long last takes after these conditions:  > 1, authorizes investigation to WOA calculation to find worldwide ideal avoids local optima. When |A|  When |A| < 1, for overhauling the position of current search operator/best arrangement is chosen. The pseudo-code of WOA technique is represented in Fig. 3.

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5. Simulation results

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5.1. Application of WOA technique

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In this paper, MATLAB/SIMULINK is used to develop the system model. A transmission delay of 50 ms (Panda, 2011) for remote input signal and sensor time delay of 15 ms is considered. After repeated run of algorithms, the following WOA parameters are used in the optimization algorithm: Population size NP = 40 and Generation G = 40. The process of optimization is run 10 times and the best estimations of fractional order SSSC-based controller parameters acquired by the WOA in 10 runs are taken as final controller parameters. To test the efficacy of the controller, different loading conditions (nominal, light and heavy) and fault clearing sequences as well as different fault disturbances are considered. The response with WOA optimized FO MISO SSSCbased damping controller with proposed multi input signal is shown with solid lines, the response with PSO optimized SSSC-based damping controller with remote input signal (Panda et al., 2008) is shown with dashed lines and the response with DE optimized SSSC-based damping controller with local input signal (Panda, 2011) is shown with dotted lines. Three cases as given below are considered: Case 1: Nominal loading (Pe = 0.85 p.u., δ0 = 51.50 ) The designed controller performance is verified at nominal loading condition under severe disturbance. A 5-cycle, 3-phase fault is considered in the transmission line near Bus 2 at t = 1.0 s. The fault is cleared by tripping the faulted line and the line is reclosed after 5-cycle. The speed deviation (ω) in p.u., power angle (δ) in degrees, real power Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 4. (a) Speed deviation response for case 1. (b) Power angle response for case 1. (c) Tie-line power response for case 1. (d) SSSC injected voltage response for case 1. (e) Speed deviation response for case 2. (f) Speed deviation response for case 3.

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flow in the transmission line (PL ) in MW and the SSSC injected voltage (Vq ) in p.u. responses for the above severe disturbance are shown in Fig. 4(a)–(d). It can be seen from Fig. 4(a)–(d) that the proposed WOA optimized FO MISO SSSC based controller provides a better damping characteristic compared to both DE optimized SSSC based controller with local input signal (Panda, 2011) and PSO optimized SSSC based controller with remote input signal (Panda et al., 2008) and also it can be found from Fig. 4(a)–(d) that the proposed approach provides better dynamic response in terms of minimum overshoot, minimum undershoot and settling time compared to both DE and PSO optimized SISO controllers. Case 2: Light loading (Pe = 0.5 p.u., δ0 = 29.50 ) Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Table 1 Q5 Controller parameters of proposed FO MISO controller.

Controller/input signal Multi input single output (MISO)/controller parameters

KPL /KPR

KdL /KdR

λ/μ

T1L /T1R

T2L /T2R

T3L /T3R

T4L /T4R

PL

72.2320

28.9650

0.7574

1.0366

0.7207

1.6253

1.6175

ω

58.9721

37.1388

0.3600

1.5681

1.6252

1.2205

0.9437

Table 2 Comparison of ITAE values for SMIB system.

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Approach: cases

FO MISO Proposed signal (x10−4 )

SISO (Panda, 2011) Local signal DE (x10−4 )

SISO (Panda et al., 2008) Remote signal PSO (x10−4 )

Case-1 Case-2 Case-3

8.2051 8.402 7.417

8.426 24.609 38.680

9.128 11.88 9.346

To examine the strength of the proposed controller, the generator loading is changed to light loading condition and a 5-cycle 3-phase fault at middle of transmission line followed by load removal near bus 1 at t = 1.0 s. The original system is restored after the fault clearance. The system response under this contingency is shown in Fig. 4(e) which evidently illustrates the strength of proposed controller for changes in operating condition and type of disturbance. Also, the proposed approach gives better transient response when consider with DE optimized controller and a slightly better transient response compared to PSO optimized controller.

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Case 3: Heavy loading (Pe = 1.0 p.u., δ0 = 60.70 ) The strength of the proposed controller is also demonstrated at heavy loading condition under small disturbance by disconnecting the load near bus1at t = 1.0 s for 100 ms with generator loading being changed to heavy loading condition. The system Response under this contingency is shown in Fig. 4(f) from which it is clear that the system is unstable with DE based SISO controller and stability of the system is maintained and oscillations are quickly damped out with proposed FO MISO controller as compared to PSO optimized SISO controller. The system responses for the above cases are provided in Fig. 4(a)–(f). It can be seen from Fig. 4(a)–(f) that proposed WOA optimized FO MISO SSSC based controller gives a superior damping characteristics compared with DE (Panda, 2011) and PSO (Panda et al., 2008) optimized SISO controllers. Table 1 represents the optimized controller parameters of the proposed method. For clear portrayal of superiority of proposed approach, performance evaluations with various input signals/systems for different cases are given in Table 2. The correlation is done utilizing integral time absolute error (ITAE) of speed deviations after the above disturbances. It is obvious from Table 2 that minimum errors are acquired with proposed approach compared with some recent methodologies.

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5.2. Extension to multi-machine power system

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The design approach of SSSC based damping controller is applied in a multi-machine (three machine six-bus) power system shown in Fig. 5. It is identical to the power system reported in references Panda et al. (2008) and Panda (2011). The system comprises of three generators partitioned into two subsystems and is associated by means of an intertie. After a disturbance, the two subsystems swing against each other bringing about instability. To enhance the stability the line is sectionalized and a SSSC is connected on the mid-point of the tie-line. The relevant information for the system is given in references Panda et al. (2008) and Panda (2011). The objective function is defined as: t   J= ( |ωL | + |ωI | ) · t · dt

(13)

0

Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 5. Multi-machine six-bus power system. Table 3 Controller parameters of proposed FO MISO controller in multi-machine power system. Controller/input signal/technique

KPL /KPR

KdL /KdR

λ/μ

T1L /T1R

T2L /T2R

T3L /T3R

T4L /T4R

Multi input single output (MISO)/proposed signal/FO

PL

99.0000

0.2298

1.2013

1.9800

1.9800

0.2298

0.2298

ω

99.0000

73.9718

0.2288

0.2489

1.1479

1.9800

0.2298

Table 4 Comparison of ITAE values for multi-machine power system.

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Approach/cases

FO MISO proposed signal

SISO local signal DE (Panda, 2011)

SISO remote signal PSO (Panda et al., 2008)

Case-1 (x10−3 ) Case-2 (x10−2 )

1.034 3.101

7.147 3.685

2.033 7.319

where, wL and ωI are the speed deviations of local and inter-area modes of oscillations respectively and t is the time range of the simulation. The same approach as given earlier is followed to design the FO MISO controller for SSSC. Speed deviations of generators G1 and G3 and line power deviation of closest Bus (i.e. Bus 5) are chosen as the input signal to the proposed FO MISO SSSC based damping controller. Table 3 signifies the optimized controller parameters of the proposed method for multi-machine system. The results for different cases of ITAE values are provided in Table 4. The errors relates to a 5-cycle, 3-phase fault close to bus 6 at t = 1 s which is cleared by 5-cycle line outage. The system response for the above case is shown in Fig. 6(a)–(b). It is evident from Fig. 6(a)–(b) that superior damping characterises are observed with proposed WOA optimized FO MISO SSSC based controller compared to both DE optimized SSSC based controller with local input signal (Panda, 2011) and PSO optimized SSSC based controller with remote input signal (Panda et al., 2008). It can also be seen from Fig. 6(a)–(b) that both inter-area and local modes of oscillations are extremely oscillatory in the lack of SSSC-based damping controller and the proposed FO MISO controller drastically improves the power stability by damping these oscillations by appropriate modulating the SSSC injected voltage. For completion, the performance of the proposed controllers is investigated under small disturbance. The load at bus 4 is detached at t = 1.0 s for 100 ms (This reproduces a small disturbance). Fig. 7(a)–(b) demonstrate the system response for the above case. It is clear from Fig. 7(a)–(b) that the proposed controller is robust and provides adequate damping even under small disturbance conditions in both inter-area and local modes of oscillations. It can be seen from Fig. 7(a)–(b) that significant improvement in transient performance in terms of damping power system oscillations and reduced settling time is obtained with proposed WOA optimized controller compared to both DE optimized SSSC based controller with local input signal (Panda, 2011) and PSO optimized SSSC based controller with remote input signal (Panda et al., 2008). Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008

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Fig. 6. (a) Inter-area mode of oscillations response for 5-cycle 3-phase fault cleared by 5 cycle line outage. (b) Local mode of oscillations response for 5-cycle 3-phase fault cleared by 5 cycle line outage.

Fig. 7. (a) Inter-area mode of oscillations response for 100 ms small disturbance. (b) Local mode of oscillations response for 100 ms small disturbance.

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6. Conclusion

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In this paper, enhancement of power system stability with the help of a fractional order MISO-SSSC based damping controller is studied in detail. The design task is considered as an optimization problem and whale optimization technique is applied for the estimation of controller parameters. The feasibility of the proposed FO MISO SSSC based damping controller in enhancing the power system stability is shown for both single machine infinite bus and three-machine six bus power systems under different severe contingencies. The superiority of the proposed controller structure and optimization method is shown by comparing results of some recently proposed methodologies like DE and PSO based SISO SSSC controller. It is observed that superior damping performance is obtained with proposed MISO controller compared to SISO controllers.

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References

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Anon, 2010. SimPowerSystems 5.2.1 User’s Guide, Available: http://www.mathworks.com. Biswas, A., Das, S., Abraham, A., Dasgupta, S., 2009. Design of fractional order PI␭ D␮ controllers with an improved differential evolution. Eng. Appl. Artif. Intell. 22 (2), 343–350.

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Please cite this article in press as: Sahu, P.R., et al., Power system stability enhancement by fractional order multi input SSSC based controller employing whale optimization algorithm. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2018.02.008